*2.4. Space Conflict Composite Index (SCCI) of PLES*

Based on the theory of landscape ecology, the characteristics of spatial complexity, spatial vulnerability, and spatial stability were used to determine the spatial conflict of the PLES index and quantitatively evaluate its intensity in the Yellow River Basin. The evaluation method using the space conflict composite index of PLES (*SCCI*) is described in [61], and the calculated *SCCI* values are normalized within the 0–1 interval. *SCCI* can be expressed as follows:

$$\text{SCCI} = \text{CI} + \text{FI} - \text{SI}$$

where *CI* is the spatial complexity index, which is quantified by using the area-weighted average patchwork fractal index (*AWMPFD*) in landscape ecology. With the rapid socioeconomic development, land development and utilization activities gradually intensify; as a result, the shapes of patches tend to be complex, and spatial utilization conflicts grow accordingly. Therefore, the area-weighted average patch fractal index (*AWMPFD*) can better characterize the degree of interference of neighboring patches to the measured patches, which reflects the degree of influence of human development and utilization activities on

the space. The higher the value, the greater the external force on the patches. The *AWMPFD* can be calculated as follows:

$$AWMPFD = \sum\_{i=1}^{m} \sum\_{j=1}^{n} \left[ \frac{2 \ln \left( 0.25 P\_{ij} \right)}{\ln \left( a\_{ij} \right)} \left( \frac{a\_{ij}}{A} \right) \right]^2$$

In this formula, *Pij* is the perimeter of the patch, *aij* is the area of the patch, *A* is the total area of the spatial type, *i* and *j* are the *j*-th spatial type in the *i*-th spatial unit; *m* is the total number of units involved in the evaluation in the study area, and *n* is the number of PLES.

*FI* is the spatial vulnerability index, which is measured by using the vulnerability of each landscape type within the study area in landscape ecology. *FI* characterizes the ability of spatial patches to resist external pressure, which directly affects the degree of spatial vulnerability. The weaker the resistance, the more vulnerable to external influence, the stronger the spatial vulnerability, and the higher the level of spatial conflict. PLES is a redistribution of the landscape types, referring to the related literature [21,22,37,44,45,62,63], the vulnerability of each type of PLES is assigned as LPS −0.1, PES −0.44, EPS −0.3, and ES −0.75. The *FI* calculation equation is as follows:

$$FI = \sum\_{i=1}^{n} F\_i \times \frac{a\_i}{S}$$

In the above formula, *Fi* is the vulnerability index of class *i* spatial type, *n* is the total number of PLES classifications, and *ai* is the area of patches of various landscape types within the unit; *S* is the total spatial area.

*SI* is the spatial stability index, which is measured through the landscape fragmentation index in landscape ecology. The main effect of spatial conflict on the regional spatial pattern can lead to landscape patch fragmentation. The more fragmented the spatial pattern, the more homogeneous the type, the less spatial stability, and the higher the intensity of the spatial conflict. The *SI* value is calculated by the following formula:

$$SI = 1 - PD$$

$$PD = \frac{n\_i}{A}$$

where *PD* is the patch density; the larger the *PD* value, the higher the fragmentation of the space, the lower the spatial stability, and the lower the stability of the corresponding spatial ecosystem. *ni* is the number of patches of type *i* spatial type in each spatial unit, and *A* is the area of each spatial unit.
